Subdivision surface creating face where it shouldn't
The reason subdivision surface is &quot;closing up&quot; the hole for the toilet basin is because you have no vertex information to continue subdividing from there.
Subdivision surface attempts to take a single face or edge and divide (hence the name) it into multiple parts. (Two parts if an edge, four if its a face)
Blender currently supports two modes of subdividing, Catmull-Clark and Simple. Catmull-Clark subdividing subdivides and attempts to smooth out the new faces by determining the proximity of each face to each other, thus creating a roundish shape. Simple subdividing subdivides each face, while retaining the original shape of the object.
If you have an unclosed portion of a mesh which you are subdividing, the dividing and smoothing of the faces on the unclosed edge will smooth and start to draw closer to each other.
In your case, you should probably either extrude the face further into the basin and close it up at the bottom, or extrude it and form a pipe or something out the back of the toilet if you don't plan to close the mesh up.
This would make the smoothing of the modifier less visible at the mouth of the toilet, and give you a better result.